Related papers: Almost-Reed--Muller Codes Achieve Constant Rates f…
Concatenation of two quantum error correcting codes with complementary sets of transversal gates can provide a means towards universal fault-tolerant computation. We first show that it is generally preferable to choose the inner code with…
We present a novel iterative decoding algorithm for Reed-Muller (RM) codes, which takes advantage of a graph representation of the code. Vertices of the considered graph correspond to codewords, with two vertices being connected by an edge…
The list decoding problem for a code asks for the maximal radius up to which any ball of that radius contains only a constant number of codewords. The list decoding radius is not well understood even for well studied codes, like…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
We construct a class of $\mathbb{Z}_2\mathbb{Z}_4$-additive cyclic codes generated by pairs of polynomials, study their algebraic structures, and obtain the generator matrix of any code in the class. Using a probabilistic method, we prove…
The objective of the paper is to establish a computable upper bound for the almost sure convergence rate for a class of ratio consensus algorithms defined via column-stochastic matrices. Our result extends the works of Iutzeler et al.…
We analyse the prequential plug-in codes relative to one-parameter exponential families M. We show that if data are sampled i.i.d. from some distribution outside M, then the redundancy of any plug-in prequential code grows at rate larger…
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank…
Almost-sure termination is an important correctness property for probabilistic programs, and a number of program logics have been developed for establishing it. However, these logics have mostly been developed for first-order programs…
Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…
We prove that there exists an absolute constant $\delta>0$ such any binary code $C\subset\{0,1\}^N$ tolerating $(1/2-\delta)N$ adversarial deletions must satisfy $|C|\le 2^{\text{poly}\log N}$ and thus have rate asymptotically approaching…
We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
This paper studies \emph{linear} and \emph{affine} error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single…
We study the density of the weights of Generalized Reed--Muller codes. Let $RM_p(r,m)$ denote the code of multivariate polynomials over $\F_p$ in $m$ variables of total degree at most $r$. We consider the case of fixed degree $r$, when we…
In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…
We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…